A Fuzzy Economic Order Quantity (EOQ) Model with Consideration of Quality Items, Inspection Errors and Sales Return

In this paper, we develop an economic order quantity model with imperfect quality, inspection errors and sales returns, where upon the arrival of order lot, 100% screening process is performed and the items of imperfect quality are sold as a single batch at a lessen price, prior to receiving the next shipment. The screening process to remove the defective items may involve two types of errors. In this article we extend the Khan et al. (2011) model by considering demand and defective rate in fuzzy sense and also sales return in our model. The objective is to determine the optimal order lot size to maximize the total profit. We use the signed distance, a ranking method for fuzzy numbers, to find the approximate of total profit per unit time in the fuzzy sense. The impact of fuzziness of fraction of defectives and demand rate on optimal solution is showed by numerical example

The Fuzzy Economic Order Quantity Problem with a Finite Production Rate and Backorders

The track of developing Economic Order Quantity (EOQ) models with uncertainties described as fuzzy numbers has been very lucrative. In this paper, a fuzzy Economic Production Quantity (EPQ) model is developed to address a specific problem in a theoretical setting. Not only is the production time finite, but also backorders are allowed. The uncertainties, in the industrial context, come from the fact that the production availability is uncertain as well as the demand. These uncertainties will be handled with fuzzy numbers and the analytical solution to the optimization problem will be obtained. A theoretical example from the process industry is also given to illustrate the new model

Fuzzy Inventory Model with Single Item Under Constant Demand and Time Dependent Holding Cost

The objective of this model is to discuss the inventory model for constant  demand and time dependent holding cost. Mathematical model has been developed for determining the optimal order quantity, the optimal cycle time and optimal total inventory cost in fuzzy environment. For defuzzification, graded unit preference integration method is used. Numerical examples are given to validate the proposed model. Sensitivity analysis is carried out to analyze the effect of changes in the optimal solution with respect to change in various parameters

Periodic Review, Push Inventory Policies for Remanufacturing

Sustainability has become a major issue in most economies, causing many leading companies to focus on product recovery and reverse logistics. This research is focused on product recovery, and in particular on production control and inventory management in the remanufacturing context. We study a remanufacturing facility that receives a stream of returned products according to a Poisson process. Demand is uncertain and also follows a Poisson process. The decision problems for the remanufacturing facility are when to release returned products to the remanufacturing line and how many new products to manufacture. We assume that remanufactured products are as good as new. In this paper, we employ a "push" policy that combines these two decisions. It is well known that the optimal policy parameters are difficult to find analytically; therefore, we develop several heuristics based on traditional inventory models. We also investigate the performance of the system as a function of return rates, backorder costs and manufacturing and remanufacturing lead times; and we develop approximate lower and upper bounds on the optimal solution. We illustrate and explain some counter-intuitive results and we test the performance of the heuristics on a set of sample problems. We find that the average error of the heuristics is quite low.inventory;reverse logistics;remanufacturing;environment;heuristics

A periodic review inventory model with stock dependent demand, permissible delay in payment and price discount on backorders

In this paper we study a periodic review inventory model with stock dependent demand. When stock on hand is zero, the inventory manager offers a price discount to customers who are willing to backorder their demand. Permissible delay in payments allowed to the inventory manager is also taken into account. Numerical examples are cited to illustrate the model

An Optimum Inventory Policy for Exponentially Deteriorating Items, Considering Multi Variate Consumption Rate with Partial Backlogging

Customer purchasing deeds may be affected by factors such as selling price and inventory level instead of demand which is considered either constant or function of a single variable which is not feasible. Consequently, in the present study, we have considered the demand rate as a function of stock-level and selling price both. In the present study, in order to develop this model, it has been assumed that items are exponentially decaying and shortages are partially backlogged and the most realistic backlogging rate is considered. In this research, we proposed a partial backlogging inventory model for exponentially decaying items considering stock and selling price dependent demand rate in fuzzy environment. In developing the model demand rate, ordering cost, purchasing cost, holding cost, back ordering cost and opportunity cost are considered as triangular fuzzy numbers. Graded mean integration representation method is used for defuzzification. A numerical example is provided to illustrate the problem. Sensitivity analysis of the optimal solution with respect to the changes in the value of system parameters is also discussed

Periodic Review, Push Inventory Policies for Remanufacturing

Sustainability has become a major issue in most economies, causing many leading companies to focus on product recovery and reverse logistics. This research is focused on product recovery, and in particular on production control and inventory management in the remanufacturing context. We study a remanufacturing facility that receives a stream of returned products according to a Poisson process. Demand is uncertain and also follows a Poisson process. The decision problems for the remanufacturing facility are when to release returned products to the remanufacturing line and how many new products to manufacture. We assume that remanufactured products are as good as new. In this paper, we employ a "push" policy that combines these two decisions. It is well known that the optimal policy parameters are difficult to find analytically; therefore, we develop several heuristics based on traditional inventory models. We also investigate the performance of the system as a function of return rates, backorder costs and manufacturing and remanufacturing lead times; and we develop approximate lower and upper bounds on the optimal solution. We illustrate and explain some counter-intuitive results and we test the performance of the heuristics on a set of sample problems. We find that the average error of the heuristics is quite low

Safety Stock Identification in Beverage Soft Drink Industries by Using Dynamic Fuzzy Logic

يعتبر تحديد المستوى الأمثل لمخزون الامان عنصرا هاما في سلسلة توريد صناعات المشروبات الغازية. في هذه البحث، تم استخدام المنطق الضبابي الديناميكي كنهج متقدم لتحديد مستوى مخزون الامان في صناعات المشروبات الغازية بهدف تقليل الكلفة الإجمالية وتلبية متطلبات العملاء. ان حدوث مشكلة النقص وعدم تلبية طلبات المستهلكين في هذه الشركات بسبب ضعف استراتيجيات الخزين المتبعة تعتبر امرا سلبيا للغاية، لذا فإن توفير استراتيجية خزين الامان المتقدمة سيؤدي إلى التغلب على هذه المشكلة خاصة بالنسبة إلى الشركات التي تعمل ضمن سياسة التصنيع لاجل التخزين. في هذا البحث تم تضمين ثلاث خطوات رئيسية هنا لتحديد مستوى الخزين الامن SS وهي أولاً، بناء مجموعة ضبابية لكل متغير، وثانيًا تحديد القيم القصوى لتمثيل مستوى الاحداثي السيني للمتغير الضبابي وكذلك تحديد قيم المدخلات الشهرية للمتغيرات، وأخيراً، تنفيذ النموذج المقترح في أداة المنطق الضبابي وذلك من خلال تطبيق برنامج Matlab. والذي يوفر الحل الموصى به ومن اجل اثبات صلاحية النموذج المقترح، تم تطبيقه لحل مشكلة في احدى شركات صناعة المشروبات الغازية وكذلك يثبت صلاحية النموذج المقترح والمناسب لهذه الصناعات. بعد تطبيق النموذج المقترح حدث تخفيض في العجز في تلبية طلبات المستهلكين بنسبة تصل الى 99.9% حيث انخفض مستوى العجز من (53,423 علبة) الى (154 علبة) فقط. أظهرت النتائج التي تم الحصول عليها من البحث الحاجة إلى اعتماد منهجيات متقدمة مثل الحوسبة الناعمة لتحديد مستوى مخزون السلامة.   The optimization of Safety stock considered an important element in the supply chain of beverage industries. In this paper, dynamic fuzzy logic was used as an advanced approach to identify the safety stock level in the beverage industries with the objective of minimizing total cost and meet with customer requirements. The problem of shortage occurred in these organizations due to poor inventory strategies which considered negative storage driver, so provide advanced safety stock identification strategy will lead to overcome this problem especially for organizations work under make to stock policy.  Three main steps are included here to identify safety stock level firstly, building of fuzzy sets for each variable, secondly, identifying max values to represent universe of discourse of variables and identify monthly input values of the variables, finally, execution of the proposed model in fuzzy logic tool embedded in Matlab software. In order to demonstrate the validity of proposed model, real data soft drink supply chain problem was presented. Reduction in stock-out of drinks about 99.9% was obtained by applying this model where the shortage was decreased from (53,423 package) to only (154 package). The obtained results of the research demonstrated the need to adopt advanced methodologies such as soft computing to identify safety stock level